[2] Horn's primary research program lies in classical logic, lexical semantics, and neo-Gricean pragmatic theory.
He mainly focused on the exploration of natural language negation and its relation to other operators.
His work in pragmatics, in particular his innovation in the theory of scalar implicature, is widely influential.
He is one of the group known as radical pragmaticists in the 1970s (along with Jerrold Sadock and others) and is a veteran of the linguistics wars[3] over generative semantics.
Notable is his use of Aristotelian notions such as the Square of Oppositions, and syllogistic logic in a modern semantic/pragmatic setting.